Spin-wave excitations (magnons) can be topologically protected. Recently, it has been demonstrated that topological magnons could be transported along the sample edge in a thermal Hall experiment (chiral edge state) [1]}. Different from the electrical Hall effect, in its thermal Hall counterpart, current is produced by a temperature gradient rather than an electric field. Thus a heat, instead of a charge, current is detected. The presence of Dzyaloshinskii-Moriya (DM) interaction mimics the role of time-reversal breaking magnetic field [1]}. Current prototypical examples of topological magnon materials include \(\text{Lu}_2\text{V}_2\text{O}_7\)  [1]}, \(\text{Cu-(1,3 bdc)}\)  [4]}, and \(\text{CrI}_3\)  [5]}. Dirac magnons have been proposed in a honeycomb ferromagnet [6]}. A chiral topological magnon insulator in three dimensions has also been studied [7]}. Thermal Hall effect has been found in various other magnetic systems such as spin liquids [8]}, [9]}, multiferroics [10]}, antiferromagnets [11]}, [12]}, [13]}, [14]}, and the pseudogap phase of a cuprate superconductor [15]}. Other neutral quasi-particles such as phonons can also exhibit thermal Hall effect  [16]}, [17]}. Magnons, topological [18]} or otherwise [19]}, play an important role in device physics, too.
